MATLAB: Solving a System of ODEs

equation solverode solver

My Input:
syms x(t) y(t) z(t)
%Units of kg and seconds
q = 1.60217662*(10^-19);
B = 2;
m_e = 1.60217662*(10*-31);
a = (q*B)/m_e;
%DiffiQ to solve
ode1 = diff(x,2) == a*diff(y);
ode2 = diff(y,2) == -a*diff(x);
ode3 = diff(z,2) == 0;
odes = [ode1; ode2; ode3];
%Solutions
S = dsolve(odes);
xSol(t) = S.x;
ySol(t) = S.y;
zSol(t) = S.z;
[xSol(t), ySol(t), zSol(t)] = dsolve(odes);
%Initial Conditions
condx1 = x(0) == 1;
condy1 = y(0) == 1;
condz1 = z(0) == 0;
%{
condvx1 = diff(x) == 1;
condvy1 = diff(y) == 2;
condvz1 = diff(z) == 2;
%}
%Plot Trajectory
t = 0:pi/50:8*pi;
plot3(ode1,ode2,ode3,'r','LineWidth',3)
My Output: Nothing. The program runs but nothing happens. I have to force close MatLab so that the script stops. I left it running for an hour to see but I am starting to think that there is another issue. Any advice is appreciated!
PS – Using Matlab R2018a and yes I purposefully commented out a section of initial conditions.

Best Answer

Try this:
...
%Initial Conditions
condx1 = x(0) == 1;
condy1 = y(0) == 1;
condz1 = z(0) == 0;
%Solutions
S = dsolve(odes, condx1, condy1, condz1);
xSol(t) = S.x;
ySol(t) = S.y;
zSol(t) = S.z;
Sx = matlabFunction(xSol);
Sy = matlabFunction(ySol);
Sz = matlabFunction(zSol);
Then evaluate the anonymous functions in terms of the variables and constants. Note that you will have to either evaluate ‘Sz’ first, then pass the result as ‘z’ or pass it as an evaluated function ‘Sz(t,Cz)’ as the ‘z’ argument.
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